give LinBox fields an allure of Givaro FieldsThis class adds the necessary requirements allowing the construction of an extension of a LinBox field. More...

#include <gf2.h>

Inherits GF2.

Public Types
typedef GF2RandIter	RandIter
	Random iterator generator type.
Public Member Functions
Object Management
Element &	init (Element &x, const int &y=0) const
	Initialization of field base element from an integer.
Element &	init (Element &x, const unsigned int &y=0) const
	Default constructor.
Element &	init (Element &x, const long &y=0) const
	Default constructor.
Element &	init (Element &x, const unsigned long &y=0) const
	Default constructor.
Element &	init (Element &x, const float &y) const
	Default constructor.
Element &	init (Element &x, const double &y) const
	Default constructor.
Element &	init (Element &x, const integer &y) const
	Default constructor.
BitVector::reference	init (BitVector::reference x, const integer &y=0) const
	Default constructor.
std::_Bit_reference	init (std::_Bit_reference x, const integer &y=0) const
	Default constructor.
integer &	convert (integer &x, Element y) const
	Conversion of field base element to a template class T.
std::_Bit_reference	convert (std::_Bit_reference x, Element y) const
	Default constructor.
template<class XXX >
XXX &	convert (XXX &x, Element y) const
	Default constructor.
Element &	assign (Element &x, Element y) const
	Assignment of one field base element to another.
BitVector::reference	assign (BitVector::reference x, Element y) const
	Default constructor.
std::_Bit_reference	assign (std::_Bit_reference x, Element y) const
	Default constructor.
integer &	cardinality (integer &c) const
	Cardinality.
integer &	characteristic (integer &c) const
	Characteristic.
Arithmetic Operations
x <- y op z; x <- op y These operations require all elements, including x, to be initialized before the operation is called. Uninitialized field base elements will give undefined results.
bool	areEqual (Element x, Element y) const
	Equality of two elements.
bool	isZero (Element x) const
	Zero equality.
bool	isOne (Element x) const
	One equality.
Element &	add (Element &x, Element y, Element z) const
	Addition.
BitVector::reference	add (BitVector::reference x, Element y, Element z) const
	Addition.
std::_Bit_reference	add (std::_Bit_reference x, Element y, Element z) const
	Addition.
Element &	sub (Element &x, Element y, Element z) const
	Subtraction.
BitVector::reference	sub (BitVector::reference x, Element y, Element z) const
	Subtraction.
std::_Bit_reference	sub (std::_Bit_reference x, Element y, Element z) const
	Subtraction.
Element &	mul (Element &x, Element y, Element z) const
	Multiplication.
BitVector::reference	mul (BitVector::reference x, Element y, Element z) const
	Multiplication.
std::_Bit_reference	mul (std::_Bit_reference x, Element y, Element z) const
	Multiplication.
Element &	div (Element &x, Element y, Element z) const
	Division.
BitVector::reference	div (BitVector::reference x, Element y, Element z) const
	Division.
std::_Bit_reference	div (std::_Bit_reference x, Element y, Element z) const
	Division.
Element &	neg (Element &x, Element y) const
	Additive Inverse (Negation).
BitVector::reference	neg (BitVector::reference x, Element y) const
	Additive Inverse (Negation).
std::_Bit_reference	neg (std::_Bit_reference x, Element y) const
	Additive Inverse (Negation).
Element &	inv (Element &x, Element y) const
	Multiplicative Inverse.
BitVector::reference	inv (BitVector::reference x, Element y) const
	Multiplicative Inverse.
std::_Bit_reference	inv (std::_Bit_reference x, Element y) const
	Multiplicative Inverse.
BitVector::reference	axpy (BitVector::reference r, Element a, Element x, Element y) const
	Natural AXPY.
std::_Bit_reference	axpy (std::_Bit_reference r, Element a, Element x, Element y) const
	Natural AXPY.
Element &	axpy (Element &r, Element a, Element x, Element y) const
	Natural AXPY.
Input/Output Operations
std::ostream &	write (std::ostream &os) const
	Print field.
std::ostream &	write (std::ostream &os, Element x) const
	Print field base element.
std::istream &	read (std::istream &is)
	Read field.
std::istream &	read (std::istream &is, Element &x) const
	Read field base element.
std::istream &	read (std::istream &is, BitVector::reference x) const
	Read field base element.
std::istream &	read (std::istream &is, std::_Bit_reference x) const
	Read field base element.
Inplace Arithmetic Operations
x <- x op y; x <- op x
Element &	addin (Element &x, Element y) const
	Inplace Addition.
BitVector::reference	addin (BitVector::reference x, Element y) const
	Inplace Addition.
std::_Bit_reference	addin (std::_Bit_reference x, Element y) const
	Inplace Addition.
Element &	subin (Element &x, Element y) const
	Inplace Subtraction.
BitVector::reference	subin (BitVector::reference x, Element y) const
	Inplace Subtraction.
std::_Bit_reference	subin (std::_Bit_reference x, Element y) const
	Inplace Subtraction.
Element &	mulin (Element &x, Element y) const
	Inplace Multiplication.
BitVector::reference	mulin (BitVector::reference x, Element y) const
	Inplace Multiplication.
Element &	mulin (std::_Bit_reference &x, Element y) const
	Inplace Multiplication.
Element &	divin (Element &x, Element y) const
	Inplace Division.
BitVector::reference	divin (BitVector::reference x, Element y) const
	Inplace Division.
std::_Bit_reference	divin (std::_Bit_reference x, Element y) const
	Inplace Division.
Element &	negin (Element &x) const
	Inplace Additive Inverse (Inplace Negation).
BitVector::reference	negin (BitVector::reference x) const
	Inplace Additive Inplace (Inplace Negation).
std::_Bit_reference	negin (std::_Bit_reference x) const
	Inplace Additive Inplace (Inplace Negation).
Element &	invin (Element &x) const
	Inplace Multiplicative Inverse.
BitVector::reference	invin (BitVector::reference x) const
	Inplace Multiplicative Inverse.
std::_Bit_reference	invin (std::_Bit_reference x) const
	Inplace Multiplicative Inverse.
Element &	axpyin (Element &r, Element a, Element x) const
	Inplace AXPY.
BitVector::reference	axpyin (BitVector::reference r, Element a, Element x) const
	Inplace AXPY.
std::_Bit_reference	axpyin (std::_Bit_reference r, Element a, Element x) const
	Inplace AXPY.
Element &	axpyin (Element &r, const std::_Bit_reference a, Element x) const
	Inplace AXPY.
std::_Bit_reference	axpyin (std::_Bit_reference r, const std::_Bit_reference a, Element x) const
	Inplace AXPY.
Element &	axpyin (Element &r, Element a, const std::_Bit_reference x) const
	Inplace AXPY.
std::_Bit_reference	axpyin (std::_Bit_reference r, Element a, const std::_Bit_reference x) const
	Inplace AXPY.
Element &	axpyin (Element &r, const std::_Bit_reference a, const std::_Bit_reference x) const
	Inplace AXPY.
std::_Bit_reference	axpyin (std::_Bit_reference r, const std::_Bit_reference a, const std::_Bit_reference x) const
	Inplace AXPY.

Detailed Description

template<>
struct LinBox::GivaroField< LinBox::GF2 >

give LinBox fields an allure of Givaro Fields

This class adds the necessary requirements allowing the construction of an extension of a LinBox field.

Member Typedef Documentation

typedef GF2RandIter RandIter [inherited]

Random iterator generator type.

It must meet the common object interface of random element generators as given in the the archetype RandIterArchetype.

Member Function Documentation

Element& init	(	Element &	x,
		const int &	y = `0`
	)		const `[inline, inherited]`

Initialization of field base element from an integer.

Behaves like C++ allocator construct. This function assumes the output field base element x has already been constructed, but that it is not already initialized. This is not a specialization of the template function because such a specialization is not allowed inside the class declaration.

Returns:: reference to field base element.

Parameters:

x	field base element to contain output (reference returned).
y	integer.

integer& convert	(	integer &	x,
		Element	y
	)		const `[inline, inherited]`

Conversion of field base element to a template class T.

This function assumes the output field base element x has already been constructed, but that it is not already initialized.

Returns:: reference to template class T.

Parameters:

x	template class T to contain output (reference returned).
y	constant field base element.

Element& assign	(	Element &	x,
		Element	y
	)		const `[inline, inherited]`

Assignment of one field base element to another.

This function assumes both field base elements have already been constructed and initialized.

Returns:: reference to x

Parameters:

x	field base element (reference returned).
y	field base element.

integer& cardinality ( integer & c ) const [inline, inherited]

Cardinality.

Return integer representing cardinality of the domain. Returns a non-negative integer for all domains with finite cardinality, and returns -1 to signify a domain of infinite cardinality.

Returns:: integer representing cardinality of the domain

integer& characteristic ( integer & c ) const [inline, inherited]

Characteristic.

Return integer representing characteristic of the domain. Returns a positive integer to all domains with finite characteristic, and returns 0 to signify a domain of infinite characteristic.

Returns:: integer representing characteristic of the domain.

bool areEqual	(	Element	x,
		Element	y
	)		const `[inline, inherited]`

Equality of two elements.

This function assumes both field base elements have already been constructed and initialized.

Returns:: boolean true if equal, false if not.

Parameters:

x	field base element
y	field base element

bool isZero ( Element x ) const [inline, inherited]

Zero equality.

Test if field base element is equal to zero. This function assumes the field base element has already been constructed and initialized.

Returns:: boolean true if equals zero, false if not.

Parameters:

x	field base element.

bool isOne ( Element x ) const [inline, inherited]

One equality.

Test if field base element is equal to one. This function assumes the field base element has already been constructed and initialized.

Returns:: boolean true if equals one, false if not.

Parameters:

x	field base element.

std::ostream& write ( std::ostream & os ) const [inline, inherited]

Print field.

Returns:: output stream to which field is written.

Parameters:

os	output stream to which field is written.

std::ostream& write	(	std::ostream &	os,
		Element	x
	)		const `[inline, inherited]`

Print field base element.

This function assumes the field base element has already been constructed and initialized.

Returns:: output stream to which field base element is written.

Parameters:

os	output stream to which field base element is written.
x	field base element.

std::istream& read ( std::istream & is ) [inline, inherited]

Read field.

Returns:: input stream from which field is read.

Parameters:

is	input stream from which field is read.

std::istream& read	(	std::istream &	is,
		Element &	x
	)		const `[inline, inherited]`

Read field base element.

Precondition:: This function assumes the field base element has already been constructed and initialized.

Returns:: input stream from which field base element is read.

Parameters:

is	input stream from which field base element is read.
x	field base element.

std::istream& read	(	std::istream &	is,
		BitVector::reference	x
	)		const `[inline, inherited]`

Read field base element.

Parameters:

is	input stream
x

Returns:: is

std::istream& read	(	std::istream &	is,
		std::_Bit_reference	x
	)		const `[inline, inherited]`

Read field base element.

Parameters:

is	input stream
x

Returns:: is

Element& add	(	Element &	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Addition.

x = y + z This function assumes all the field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.
z	field base element.

BitVector::reference add	(	BitVector::reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Addition.

Parameters:

x
y
z

std::_Bit_reference add	(	std::_Bit_reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Addition.

Parameters:

x
y
z

Element& sub	(	Element &	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Subtraction.

x = y - z This function assumes all the field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.
z	field base element.

BitVector::reference sub	(	BitVector::reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Subtraction.

Parameters:

x
y
z

std::_Bit_reference sub	(	std::_Bit_reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Subtraction.

Parameters:

x
y
z

Element& mul	(	Element &	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Multiplication.

x = y * z This function assumes all the field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.
z	field base element.

BitVector::reference mul	(	BitVector::reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Multiplication.

Parameters:

x
y
z

std::_Bit_reference mul	(	std::_Bit_reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Multiplication.

Parameters:

x
y
z

Element& div	(	Element &	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Division.

x = y / z This function assumes all the field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.
z	field base element.

Bug:: z is unused

BitVector::reference div	(	BitVector::reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Division.

Parameters:

x
y
z

std::_Bit_reference div	(	std::_Bit_reference	x,
		Element	y,
		Element	z
	)		const `[inline, inherited]`

Division.

Parameters:

x
y
z

Element& neg	(	Element &	x,
		Element	y
	)		const `[inline, inherited]`

Additive Inverse (Negation).

x = - y This function assumes both field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.

BitVector::reference neg	(	BitVector::reference	x,
		Element	y
	)		const `[inline, inherited]`

Additive Inverse (Negation).

Returns:: reference to x.

Parameters:

x
y

std::_Bit_reference neg	(	std::_Bit_reference	x,
		Element	y
	)		const `[inline, inherited]`

Additive Inverse (Negation).

Returns:: reference to x.

Parameters:

x
y

Element& inv	(	Element &	x,
		Element	y
	)		const `[inline, inherited]`

Multiplicative Inverse.

x = 1 / y This function assumes both field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.

BitVector::reference inv	(	BitVector::reference	x,
		Element	y
	)		const `[inline, inherited]`

Multiplicative Inverse.

Returns:: reference to x.

Parameters:

x
y

std::_Bit_reference inv	(	std::_Bit_reference	x,
		Element	y
	)		const `[inline, inherited]`

Multiplicative Inverse.

Returns:: reference to x.

Parameters:

x
y

BitVector::reference axpy	(	BitVector::reference	r,
		Element	a,
		Element	x,
		Element	y
	)		const `[inline, inherited]`

Natural AXPY.

r = a * x + y This function assumes all field elements have already been constructed and initialized.

Returns:: reference to r.

Parameters:

r	field element (reference returned).
a	field element.
x	field element.
y	field element.

std::_Bit_reference axpy	(	std::_Bit_reference	r,
		Element	a,
		Element	x,
		Element	y
	)		const `[inline, inherited]`

Natural AXPY.

Returns:: reference to r.

Parameters:

r
a
x
y

Element& axpy	(	Element &	r,
		Element	a,
		Element	x,
		Element	y
	)		const `[inline, inherited]`

Natural AXPY.

Returns:: reference to r.

Parameters:

r
a
x
y

Element& addin	(	Element &	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Addition.

x += y This function assumes both field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.

BitVector::reference addin	(	BitVector::reference	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Addition.

Returns:: reference to x.

Parameters:

x
y

std::_Bit_reference addin	(	std::_Bit_reference	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Addition.

Returns:: reference to x.

Parameters:

x
y

Element& subin	(	Element &	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Subtraction.

x -= y This function assumes both field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.

BitVector::reference subin	(	BitVector::reference	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Subtraction.

Returns:: reference to x.

Parameters:

x
y

std::_Bit_reference subin	(	std::_Bit_reference	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Subtraction.

Returns:: reference to x.

Parameters:

x
y

Element& mulin	(	Element &	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Multiplication.

x *= y This function assumes both field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.

BitVector::reference mulin	(	BitVector::reference	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Multiplication.

Returns:: reference to x.

Parameters:

x
y

Element& mulin	(	std::_Bit_reference &	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Multiplication.

Returns:: reference to x.

Parameters:

x
y

Element& divin	(	Element &	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Division.

x /= y This function assumes both field base elements have already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).
y	field base element.

Bug:: y is unused

BitVector::reference divin	(	BitVector::reference	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Division.

Returns:: reference to x.

Parameters:

x
y

Bug:: y is unused

std::_Bit_reference divin	(	std::_Bit_reference	x,
		Element	y
	)		const `[inline, inherited]`

Inplace Division.

Returns:: reference to x.

Parameters:

x
y

Bug:: y is unused

Element& negin ( Element & x ) const [inline, inherited]

Inplace Additive Inverse (Inplace Negation).

x = - x This function assumes the field base element has already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).

BitVector::reference negin ( BitVector::reference x ) const [inline, inherited]

Inplace Additive Inplace (Inplace Negation).

Returns:: reference to x.

Parameters:

x

Bug:: y is unused

std::_Bit_reference negin ( std::_Bit_reference x ) const [inline, inherited]

Inplace Additive Inplace (Inplace Negation).

Returns:: reference to x.

Parameters:

x

Bug:: y is unused

Element& invin ( Element & x ) const [inline, inherited]

Inplace Multiplicative Inverse.

x = 1 / x This function assumes the field base elementhas already been constructed and initialized.

Returns:: reference to x.

Parameters:

x	field base element (reference returned).

BitVector::reference invin ( BitVector::reference x ) const [inline, inherited]

Inplace Multiplicative Inverse.

Returns:: reference to x.

Parameters:

x

std::_Bit_reference invin ( std::_Bit_reference x ) const [inline, inherited]

Inplace Multiplicative Inverse.

Returns:: reference to x.

Parameters:

x

Element& axpyin	(	Element &	r,
		Element	a,
		Element	x
	)		const `[inline, inherited]`

Inplace AXPY.

r += a * x This function assumes all field elements have already been constructed and initialized. Purely virtual

Returns:: reference to r.

Parameters:

r	field element (reference returned).
a	field element.
x	field element.

BitVector::reference axpyin	(	BitVector::reference	r,
		Element	a,
		Element	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

std::_Bit_reference axpyin	(	std::_Bit_reference	r,
		Element	a,
		Element	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

Element& axpyin	(	Element &	r,
		const std::_Bit_reference	a,
		Element	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

std::_Bit_reference axpyin	(	std::_Bit_reference	r,
		const std::_Bit_reference	a,
		Element	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

Element& axpyin	(	Element &	r,
		Element	a,
		const std::_Bit_reference	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

std::_Bit_reference axpyin	(	std::_Bit_reference	r,
		Element	a,
		const std::_Bit_reference	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

Element& axpyin	(	Element &	r,
		const std::_Bit_reference	a,
		const std::_Bit_reference	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

std::_Bit_reference axpyin	(	std::_Bit_reference	r,
		const std::_Bit_reference	a,
		const std::_Bit_reference	x
	)		const `[inline, inherited]`

Inplace AXPY.

Returns:: reference to r.

Parameters:

r
a
x

The documentation for this struct was generated from the following file:

field/gf2.h

Public Types

Public Member Functions

Detailed Description

template<> struct LinBox::GivaroField< LinBox::GF2 >

Member Typedef Documentation

Member Function Documentation

template<>
struct LinBox::GivaroField< LinBox::GF2 >